Quantized alternating integrable mappings

Abstract

A new alternating quantum integrable map is presented (i.e. a non-autonomous quantum integrable map whose sole time-dependence is of the form ). For a certain parameter reduction, the map becomes autonomous, and is, in fact, the quantum version of a recently introduced close-to-the-identity integrable map. The quantum version of the recently introduced alternating McMillan map is also given. The unitary evolution operator is given explicitly for both maps, hence, both maps give a true quantum mechanical time evolution.